four more than twice a number is greater than negative eighteen. Solve the inequality for the unknown number

In Illinois, 10 % of all drivers arrested for DUI (Driving Under the Influence) are repeat offenders; that is, they have been ar

docker41 [41]

Answer:

a) P(X=5) = 0.065

b) P(X≥1) = 0.928

c) The mean number of repeat offenders is 3.

d) The standard deviation of the number of repeat offenders is 2.

Step-by-step explanation:

n = 25

p = 10% = 0.10

q = 1-p

= 1-0.1

q=0.9

a) Find P(X =5)

Using the binomial distribution formula:

P(X = x) = ⁿCˣ pˣ qⁿ⁻ˣ

where p = probability of success

q = probability of failure

n = total number of trials

x = no. of successful trials

P(X=5) = ²⁵C₅ (0.1)⁵ (0.9)²⁵⁻⁵

= 0.0645 ≅ 0.065

P(X=5) = 0.065

b) We need to find the probability that at least one person is a repeat offender which means at most there can be 25 repeat offenders hence, we need to compute the probability for all values ranging from 1 to 25. The easy way to solve this problem is to find out the probability of less than one repeat offender and then subtract the value from the total probability (i.e. 1).

P(X≥1) = 1 - P(X<1)

= 1 - P(X =0)

= 1 - ²⁵C₀ (0.1)⁰ (0.9)²⁵⁻⁰

= 1 - 0.072

P(X≥1) = 0.928

c) The mean of the binomial distribution is:

μ = np

So, the mean number of repeat offenders can be computed as:

μ = (25)(0.10)

μ = 2.5 ≅ 3

The mean number of repeat offenders is 3.

d) The standard deviation of the binomial distribution is:

σ = √npq

So, the standard deviation of the number of repeat offenders can be computed as:

σ = √(25)(0.1)(0.9)

= √2.25

σ = 1.5 ≅ 2

The standard deviation of the number of repeat offenders is 2.

7 0

2 years ago

In a plane, line b is parallel to line f, line f is parallel to line g, and line h is perpendicular to line b. Which of the foll

dexar [7]

Answer: f is Parralel to g

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers

The function h(x) is given below.

zavuch27 [327]

The inverse function will be h⁻¹(x) = {(–5, 3), (–7, 5), (–9, 6), (–12, 10), (–16, 12)}. Then the correct option is B.

<h3>What is inverse of a function?</h3>

Suppose that the given function is

f:X → Y

Then the inverse of the considered function will be

f⁻¹: Y → X

The function h(x) is given below.

h(x) = {(3, –5), (5, –7), (6, –9), (10, –12), (12, –16)}

Then the coordinate of the inverse function gets swapped.

h⁻¹(x) = {(–5, 3), (–7, 5), (–9, 6), (–12, 10), (–16, 12)}

Then the correct option is B.

Learn more about inverse function here:

brainly.com/question/19425567

#SPJ1

8 0

1 year ago

Triangle A E C is shown. Line segment B D is drawn near point C to form triangle B D C.

AVprozaik [17]

∠BDC and ∠AED are right angles, is a piece of additional information is appropriate to prove △ CEA ~ △ CDB

Triangle AEC is shown. Line segment B, D is drawn near point C to form triangle BDC.

<h3> What are Similar triangles?</h3>

Similar triangles, are those triangles which have similar properties,i.e. angles and proportionality of sides.

Image is attached below,
as shown in figure
∡ACE = ∡BCD ( common angle )
∡AED = ∡BDC ( since AE and BD are perpendicular to same line EC and make right angles as E and C)
∡EAC =- ∡DBC ( corresponding angles because AE and BD are parallel lines)

Thus, △CEA ~ △CDB , because of the two perpendiculars AE and BD.

Learn more about similar triangles here:
brainly.com/question/25882965

#SPJ1

3 0

1 year ago

Plss it due today plssss don’t just take the points

Murljashka [212]

Answer:

Step-by-step explanation:

3x + 11 + x - 9 + 56 = 180

4x + 58 = 180

4x = 122

x = 30.5

6 0

2 years ago